Question

A red car and a blue car are traveling at the same speed. The red car drives 3 hours. The blue car drives another half hour and goes 25 more miles. Which equation can be solved to find how fast the cars are going?

Answer 1

To find how fast the cars are going, we can set up a proportion using the given information and solve for x. The equation that can be solved is 7.5x^2 - 25x = 0. The solutions to the equation are x = 5/3 or x = 10/3.

Step-by-step explanation:

To find how fast the cars are going, we need to set up a proportion using the information given. Let's say the speed of each car is x miles per hour. The red car drives for 3 hours, so it travels 3x miles. The blue car drives for 3.5 hours (3 hours for the red car plus the additional half hour) and goes 25 more miles than the red car, so it travels (3x + 25) miles. Since both cars are traveling at the same speed, we can set up the proportion:

3x / x = (3x + 25) / (3.5x)

Cross multiplying gives us:

3x * (3.5x) = x * (3x + 25)

Simplifying further, we get:

10.5x^2 = 3x^2 + 25x

Combining like terms and rearranging the equation, we have:

7.5x^2 - 25x = 0

Using the quadratic formula, we can solve for x:

x = (-(-25) ± sqrt((-25)^2 - 4 * 7.5 * 0)) / (2 * 7.5)

Simplifying further, we get:

x = (25 ± sqrt(625)) / 15

Therefore, the equation that can be solved to find how fast the cars are going is:

x = (25 ± 25) / 15

or

x = 5/3 or 10/3